A035628 - OEIS

%I #18 Aug 16 2020 17:07:25

%S 0,0,0,0,0,0,1,0,1,0,1,3,1,3,1,3,7,3,8,3,8,14,8,17,8,18,26,18,33,18,

%T 36,47,37,61,37,68,81,71,106,72,121,138,128,181,131,209,228,224,297,

%U 231,347,372,376,482,391,566,592,619,760,648,898,934,989,1188,1043

%N Number of partitions of n into parts 5k and 5k+2 with at least one part of each type.

%H Robert Price, <a href="/A035628/b035628.txt">Table of n, a(n) for n = 1..1000</a>

%F G.f.: (-1 + 1/Product_{k>=0} (1-x^(5k+2)))*(-1 + 1/Product_{k>=1} (1-x^(5k))). - _Robert Price_, Aug 07 2020

%t nmax = 65; s1 = Range[1, nmax/5]*5; s2 = Range[0, nmax/5]*5 + 2;

%t Table[Count[IntegerPartitions[n, All, s1~Join~s2],

%t x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 1, nmax}] (* _Robert Price_, Aug 06 2020 *)

%t nmax = 65; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(5 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(5 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* _Robert Price_, Aug 06 2020 *)

%Y Cf. A035441-A035468, A035618-A035627, A035629-A035699.

%K nonn

%O 1,12

%A _Olivier Gérard_